Author

Barinder S. Banwait

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Preprint Sep 2026

Second derivatives of $p$-adic $L$-functions and the Shafarevich--Tate group of rank-two CM elliptic curves

For an elliptic curve $E/\mathbb{Q}$ of rank two with complex multiplication, Coates, Liang and Sujatha gave a criterion for the vanishing of $Sha(E/\mathbb{Q})[p^\infty]$ at a good ordinary prime $p$ and applied it to five such curves for $p<30{,}000$. We prove a cyclotomic criterion of the same kind: outside an expli...

Barinder S. Banwait · 0 citations

#machine learning Jul 2026

Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves

We investigate the extent to which the coefficients $(w_1,w_2,w_3,w_4,w_6)$ of the reduced minimal Weierstrass model of an elliptic curve $E/\mathbb{Q}$ are determined by the Dirichlet coefficients $a_n(E)$ of its $L$-function, whose values at primes of good reduction are the Frobenius traces of $E$. We prove that $w_1...

Barinder S. Banwait, Xiao-Yu Huang, Kyu-Hwan Lee et al. · arXiv.org · 0 citations